To add new points, right-click to select the line to which your new point will be added, and then click Add Point. This action places a point on the selected line equidistant from the endpoints of that line, creating two separate lines. You can now manipulate this new point as described in Moving and Locking Points.
To remove an existing point, right-click to select the point, and then click Delete from the context menu. This action will remove the point and the two connecting lines, and will replace them with a new line connecting the points adjacent to the one removed.